Intraocular lenses or IOLs are routinely used in most cataract surgery cases to correct aphakia. They are called Aphakic IOLs. IOLs are also used in the refractive surgery to correct refractive error of phakic subjects. These lenses are called Phakic IOLs or PIOLs. Another type of IOLs is toric IOL which includes torix, i.e. surface with cylinder power, on one of its surfaces. More recently a multifocal optic was introduced and the corresponding lenses are called Multifocal IOLs or MIOLs. The term IOL is used in reference to all above types of intraocular lenses through out the text below.
The average pupil size of the eye at normal photopic lighting condition is around 3 mm diameter and increases or dilates to about 5 mm diameter or even higher al low light condition called mesopic condition. Changes in pupil size contribute to imaging quality of the eye—the image quality usually reduces with pupil dilation. In addition to pupil size the lens decentration (radial translation) or tilt (axial rotation), jointly called misalignments, significantly contribute to the image quality also. A dioptric power of the intraocular lens is selected for the implantation per photopic conditions, i.e. average pupil size of about 3 mm. Fortunately, with present day surgical technique, common lens misalignment does not practically impact the image quality for up to about 4 mm pupil diameter but then the issue arises with the pupil dilation above 4 mm diameter which usually occurs with the reduction in lighting.
The final quality of the retinal image in patients with IOLs depends upon the aberrations of the eye. Even in the perfectly centered position of spherical IOL, there is still spherical aberration. Burk in the U.S. Pat. No. 4,504,982 was first who addressed this type of aberration. He suggested an aspheric lens that had a plurality of radii from the apex to the edge with the radii generally increasing away from the apex. This aspheric lens eliminates most of the spherical aberrations occurred in the lens centered position by the use of the progressively longer radii towards the outer zone of the lens. Among aphakic lenses, Tecnis® IOL was one of the first commonly utilized aspheric IOL that relies on the above principle. As it was reported by J. T. Holliday, et al., “A New Intraocular Lens Designed to Reduce Spherical Aberration of Pseudophakic Eyes,” Journal of Refractive Surgery 2002, the Tecnis® IOL has been found to improve visual contrast sensitivity at dilated pupils.
The Tecnis® Z9000 IOL was designed to correct the average corneal spherical aberrations present in the cataract population and mathematically defined as prolate elliptical surface with corneal asphericity Q=−0.26. However, Tecnis® type lenses generally require precise positioning in the capsular bag to provide improved optical quality over a spherical IOL, see “Prospective Randomized Trial of an Anterior Surface Modified Prolate Intraocular Lens,” Journal of Refractive surgery, Vo. 18, November/December 2002. Slight lens misalignment greatly reduces the effectiveness of the lens with dilated pupils.
In order to manage to some degree imaging sensitivity to lens misalignment, AcrySol® lens was introduced with only partial corneal spherical aberration compensation. Nevertheless, tilt or decentration with either this lens or Tecnis® type lens can still lead to significant distortions that will be worse than they may have demonstrated by a conventional spherical lens.
The described above aspherization was further expanded in the US Application No. 20060116764 where the aspherization was incorporated into the base profile over which diffractive echelettes are superimposed on in order to improve image contrast over the lens with spherical base profile of the equivalent power. In order to achieve image contrast improvement by base profile aspherization the diffractive zone with the corresponding aspheric base profile, must be above approximately 4 mm diameter because below about 4 mm diameter a spherical base profile incorporates only small magnitude of aberrations and thus provides close to diffractive-limited performance for an equivalent aspheric monofocal lens. Thus, base surface profile aspherization as described in the above disclosure, technically makes sense only for full aperture diffractive optic occupying above 4 mm diameter where image contrast improvement can be achieved. It will be shown in the invention description below that one can achieve improvement in contrast over corresponding spherical base profile even in case of partial surface diffractive zone occupying below of about 4 mm diameter if both base profile and surface periphery outside the diffractive zone are aspherized or even if only surface periphery is properly aspherized.
The SofPort® Advanced Optics (AO) aberration-free aspheric intraocular lens was also introduced. The lens was designed so that the lens itself had no spherical aberration. Though it reduced sensitivity to lens misalignment, its image quality in close to centered lens position was not much differ from one offered by conventional spherical lens of the equivalent power.
The common design of the aspheric IOLs that only target spherical aberration is their prolate surface shape, i.e. the shape is such that the radii generally increasing away from the apex (surface vertex) as originally suggested by Burk.
It is believed that “typical” magnitude of IOL misalignment is less than about 1.0 mm decentration and less than about 10 degrees tilt, these is so called “realistic clinical condition”. Therefore, a benefit of aspheric prolate surface lenses that are designed to compensate only for spherical aberration is limited because the imaging quality of such lenses may reduce below the imaging quality of the equivalent power spherical lens within the realistic clinical condition.
Lang et al in U.S. Pat. No. 7,381,221 introduced a multi-zonal monofocal ophthalmic lens that is designed to be less sensitive to lens decentration. The proposed lens is designed as a combination of prolate zones with different asphericities and powers. The lens was designed to compensate for some effect of decentration that results in a shift in focus position but doesn't address a possible lens tilt or a combination of tilt and decentration which is more common clinically.
Thus, there is the need for a better solution for aspheric optic that would maintain the imaging superiority over conventions spherical lens of the equivalent power within the realistic clinical condition.
In order to explain the invention the following background information is also provided.
It has been a common approach to describe aspheric lens aberrations in terms of wavefront aberrations. Wavefront Error can be represented mathematically as Zernike Polynomial Decomposition W(ρ,θ)=Σan,mZnm(ρ,θ), where Znm(ρ,θ) are Zernike radial polynomials of n-order and m-frequency and an,m are Zernike Coefficients as the measure of wavefront aberrations and commonly called “aberrations”. In this Zernike Polynomial Decomposition, 2nd order aberrations are called Low Order Aberrations (LOA) which includes defocus and astigmatism, and aberrations above 2nd order are called High Order Aberrations (HOA). They include spherical aberration, coma, trefold, etc.
There is certain misconception about wavefront aberrations as applied to ocular imaging because they are mathematical abstraction and do not directly represent light distribution at the retina in a form of spot diagram. Their impact on the image quality can only be measured through their relationship with ray aberrations which directly relate to the light distribution at the retinal image.
The key benefit of wavefront aberrations lies in the ability to assess a relative contribution on the optical quality by different wavefront aberrations. This is because Zernike radial polynomials are normalized orthogonal set of functions and their coefficients which are called “wavefront aberration”, can be easily combined into groups by Root Mean Square (RMS) per formula RMS2=Σ(an,m)2. For instance, one can combine Low Order Aberration into RMSLOA and high order aberrations into RMSHOA in order to assess their relative contributions to the optical quality. Low order wavefront aberrations are related to ray aberrations such as defocus and astigmatism jointly called refractive error which is correctable by conventional optical aids such as glasses, contact lenses and IOLs, but high order aberrations generally are not.
In order to understand a relationship between the aberrations and light distribution at the retina, optically called spot diagram, one has to include ray aberrations. The relationship between wavefront and ray aberrations can be found for instance in James C Wyant, “Basic Wavefront Aberration Theory for Optical Metrology”, Applied Optics and Optical Engineering, Vol. XI, Chapter 1, 1992.
Wavefront error is usually defined at the Entrance Pupil of the optical system as W(x,y), where x, y are pupil Cartesian coordinates. Assuming the wavefront error W(x,y) is relatively small and the angle between the reference and aberrated wavefronts is also small, FIG. 2. This angle αx is called angular aberration of the ray and defined by the first derivative of the wavefront error
      α    x    =                    -                  ∂                      W            ⁡                          (                              x                ,                y                            )                                                  n        ⁢                  ∂          x                      .  The corresponding transverse aberration Tx and longitudinal aberration L of the ray are also defined by the first derivative of the wavefront aberration:
            T      x        =                            R          w                ⁢                  α          x                    =                        -                      R            w                          =                              ∂                          W              ⁡                              (                                  x                  ,                  y                                )                                                          n            ⁢                          ∂              x                                            ;the same for Ty; as transverse ray aberrations along x and y-coordinates at the pupil. The ratio of the longitudinal ray aberration and transverse ray aberration and
      L          T      x        ≈            R      w              (              x        -                  T          x                    )        ≈            R      w        x  and
  L  ≈            -                        R          w          2                x              ⁢                            ∂                      W            ⁡                          (                              x                ,                y                            )                                                n          ⁢                      ∂            x                              .      It is resulted in the difference between the distances to the aberrated ray focus and perfect ray focus where foci are defined as the points of intersections of these rays with the optical axis.
Thus, wavefront aberrations have abstract mathematical meaning of the coefficients in Zernike Polynomial Decomposition but at certain low enough orders of the wavefront aberrations such defocus, astigmatism, spherical aberration and coma, they correlate per above equations with the ray aberrations under the same names. Ray aberrations have physical meaning of light energy travel and can be geometrically interpreted by light rays distribution at the retina. This allows to describing the invention in geometrical terms which are more perceptible than abstract mathematical terms of wavefront aberrations.
In summary, there are two measures of vision quality: (1) pupil based which are wavefront related such as wavefront aberrations and RMS because wavefront is defined at the pupil plane of the eye, and (2) image plane based such as PSF (Point Spread Function), Strehl Ratio and MTF related which are derived from the spot diagram at the image plane, i.e. an image of the point object at the retina. Aberrometry used for measuring eye aberrations directly measures spot diagram and derives all other measures from it.
Pupil based measures are in good correlation with vision quality for 3 mm pupil and smaller because the aberrations are only small fraction of the wavelength. At this condition of the nominal eye is almost diffractive limited system and its Strehl Raito is 0.8 or higher. At this condition there is a linear relationship between Strehl Ratio and (RMS2), i.e. pupil based measure lineally relates to pupil based measure and one can use either one for image quality analysis.
It has been shown that for larger pupils with large aberrations, pupil based measures are in poor correlation with vision quality and image plane based measures are much better to use in these conditions. At very large aberrations, spot diagram size becomes a dominant factor. Thus, it is more appropriate to utilize spot diagram and corresponding ray aberrations for image quality analysis at large pupil and lens misalignment where the aberrations are significant.
The simplest ray aberration to interpret is longitudinal ray aberration as being one-dimensional characteristic as the transverse (tangential) ray aberration is defined by two-dimensional characteristic. For optically centered system, longitudinal ray aberration is also called longitudinal spherical aberration or LSA. One can divide the entrance pupil or lens surface along, say x-meridian, into the regions. Each region can be characterized by its own longitudinal spherical aberration and the total spot diagram can be analyzed as a combination of spot diagrams from the regions. Below we will use ray aberrations and specifically longitudinal ray aberration for describing the invention.